The vortex filament equation as a pseudorandom generator

Abstract

In this paper, we consider the evolution of the so-called vortex filament equation (VFE), \begin{equation*} \mathbf X_t = \mathbf X_s\wedge\mathbf X_{ss}, \end{equation*} taking a planar regular polygon of $M$ sides as initial datum. We study VFE from a completely novel point of view: that of an evolution equation which yields a very good generator of pseudorandom numbers in a completely natural way. This essential randomness of VFE is in agreement with the randomness of the physical phenomena upon which it is based.

17 pages in Acta Applicandae Mathematicae, 2014

References in corpus (3)

• Vortex Filament Equation for a Regular Polygon
• On the stability of a singular vortex dynamics
• Stability of the selfsimilar dynamics of a vortex filament

Cited by in corpus (1)

• On the Relationship between the One-Corner Problem and the $M$-Corner Problem for the Vortex Filament Equation